Let f(x) = x* – 4x³ + 4x2 + 12x – 21. Given that 2 – V3i is a root of f(x), factor f(x) into a product of irreducible polynomials in C[x], R[x] and Q[x].

Q: 3. For the function g(x) = x³ – 2x? – 11x + 12, use long division to determine whether each of the…

A: we devide the polynomial by given factor and if we get remainder zero then this given factor is…

Q: Let a be a root of the polynomial x3+x+3, which is irreducible over Q. The polynomial x2-2 is also…

A: Given: a is a root of the polynomial x3+x+3, which is irreducible over ℚ. The polynomial x2-2 is…

Q: Let p > 2 be a prime number. If f(x) = 1' + x* + x² - x +1 € Z,[F] is divisible by the polynomial z…

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Q: Letf(x), g(x) and h(x) be quadratic polynomials having positive leading coefficients and real and…

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Q: A monic cubic polynomial has zeros 2 and (-1)/2±√11/2 i. Find the polynomial.

A: Given zeros are 2, -12±112i let a=-2, b=-12+112i, c=-12-112i let x be the variable of the…

Q: Two polynomials are defined in MATLAB as >>p=[5 03 2 0]; q= 0 -1]; lo find the zeros of T(s) =…

A: Matlab is a programming and numerical platform to compute values, analyze , create model.

Q: Let f(r) = (8+2)r Find the third Maclaurin polynomial for f. Use the polynomial in (a) to evaluate…

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Q: Consider the polynomial equation of P(r) = 0 where P(x) = #* – a* – ² – a – - 2. - T (a) What are…

A: The given polynomial is Px=x4-x3-x2-x-2.

Q: Use the Intermediate Value Theorem to determine whether the polynomial function has a zero in the…

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Q: Find the linear polynomial p(x) = a1x + ao, that interpolates the two points with coordinates (3, 0)…

A: Given query is to find the equation of the line.

Q: (10) 3 f(-1) = 1, f(1) = f(0) = 4, and f(r2) = f(1) = 1, to construct interpolating polynomials of…

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Q: -25 – 5x4 + 5x³ – 11æ² – 21x – 40

A: Given: f(x)=-x5-5x4+5x3-11x2-21x-40 To find: f'(x) and f''(x).

Q: Algebraically, find all zeros of f(x) = 8x3-6x2-36x + 27 in simplest form, %3D 4. Format Font - Size…

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Q: 3. [32] −1 4-3 4. 5. [. |_3 -4 2 1 2 -1 4,

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Q: Find Ao, A1, and Az in rewriting the function of f(x=2vx 0マx in terms of Lagure polynomial ョーの

A: Given: Let us consider the given function  fx=2x       x≥00             x<0 and the Lagure…

Q: Solve using method of undetermined coefficients: y" + y' - 2y = x². %3D

A: Solution :-

Q: Give an interpolating polynomial for f(x) = ²x at x = 0, 1 and 3. Evaluate it at x = 2 and give the…

A: The given function is: fx=e2x. The points are: x=0,1,3. Find the Lagrange polynomials.…

Q: If f(x) is a polynomial function satisfying f(x) ·ƒ ( ² ) = f(x) + f ( ² ) a and f(4) = 65, then…

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Q: For the polynomial below, -1 is a zero of multiplicity two. 4 f(x)=x"+4x+10x+12x+5 Express f (x) as…

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Q: Compute the first 5 Legendre Polynomials, Po(x), P₁(x), -P₁(x). (These These are > Solutions, P,…

A: What is Legendre Polynomial: Legendre polynomial is a collection of orthogonal polynomials of degree…

Q: Show that f (x) = x2 + 3x−1 and g(x) = 3x3 − 9x + x−2 are rational functions—that is, quotients of…

A: To show: That the functions are rational function: Given: The functions are fx=x2+3x-1 and…

Q: Let f(x) = x4 − 9x3 + 23x2 − 15x − 10. Find an integer n1 so that f(x) has a root between x = n1 and…

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Q: Prove that f(x) = 5x? + 3x – 26 is 0(x²). %3D

A: Given: f(x) = 5x2 + 3x – 26  is  θ(x 2).

Q: Prove that you can find a polynomial p(x) = Ax2 + Bx + C that passes through any three points (x1,…

A: we have to prove that we can always find a polynomial p(x) = Ax2 + Bx + C that  passes through any…

Q: 3. Is the polynomial f(x) = 2x° + 30r – 150 € Q(r] reducible or irreducible over Q? In either case,…

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Q: Find the zero(s) of the polynomial ³ - x²-3x+3.

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